Mathematical Modelling of Motion Detection in Fly’s Visual Cortex

Visual motion detection is one of the most active areas in neuroscience today. In this paper, we investigate the mechanism of motion-detection in the fly’s visual cortex.

First, we investigate how the direction signals of the moving objects are encoded in the visual cortex of fly. Several differential equations are derived to model the dendrites which carry information to the tangential cells in the visual cortex of fly and to model the dynamics in the synaptic inputs.  By tracing the trajectory of the solution of one of the differential equations together with solving the other differential equations, a conclusion is drawn which can explain how the visual system of fly encodes the motion signal like the change of the direction.

In the second part of the paper, we study the mechanism underlying the “vector addition” as stated in “population vector” hypothesis.  Mathematical models are built for a descending neuron and two tangential cells.  Partial differential equations are derived and solved to find out the relation between the input and output of the descending neuron. We come to the conclusion that if the visual cortex of fly does perform vector addition, this ability should be mainly attributed to the special arrangement of the synaptic locations on the dendrites.

In the third part of the paper, a hypothesis is proposed about how the brain of fly reconstructs the motion trajectory based on the firing rates of the neurons in the brain.

In summary, by mathematical modelling of the visual systems in the fly, several conclusions are drawn which can be supported by the results obtained from biological experiments.  Hence, these mathematical models are close simulation of biological neural systems.